There is a recurrent need to determine the electrostatic interaction capacitance between two conducting parts when designing integrated circuits. The determination is carried out in particular to characterize capacitors used in circuits, or to characterize electrostatic interactions between various conducting parts such as, for example, electrical signal transmission tracks. This is because such interactions introduce delays in the electrical operation of the circuit incorporating these conducting parts. In the case of electrical signal transmission tracks, these delays reduce the signal transmission rate.
A first method of determining such capacitances consists in solving the fundamental electrostatic equations known to those skilled in the art. These equations may especially be reduced to the Laplace equation relating to the electrostatic potential, combined with boundary conditions suitable for the conducting parts envisaged. However, an exact solution of the problem thus posed is possible only for simple geometrical configurations of the conducting parts, which in general do not correspond to actual configurations used in integrated circuits.
Methods for the approximate solution of the Laplace equation, especially by finite elements, have been developed which allow the electrostatic potential to be calculated at defined points in the vicinity of the conducting parts. An estimate of the capacitance between two conducting parts can therefore be easily deduced therefrom. In order for this estimate to be sufficiently accurate, such methods require the electrostatic potential to be calculated at a very large number of points. Consequently, they are tedious and lengthy, they require the use of computing stations of high computing power, and they are expensive in terms of computing time.
To reduce the amount of computing needed for finite element methods, it is common practice to make approximations and simplifications which impair the accuracy of the estimate obtained. These approximations especially comprise simplifications of the configuration of the conducting parts, such as, the fact of neglecting the thickness of conducting plates with respect to their length and their width. The estimate of the capacitance calculated in this way therefore often differs by 10%, or even 14%, from the actual capacitance, when the latter can, for example, be determined experimentally.
In general, the relative difference between the capacitance thus estimated and the actual capacitance of an integrated component increases when the size of said component decreases. This increase results especially from contributions neglected in the calculation of the capacitance, the magnitude of which increases relative to the contributions taken into account in the calculation, when the component becomes smaller. Such neglected contributions are, for example, associated with the edges of conducting parts. The increasing integration of electronic circuits fabricated at the present time consequently requires accurate methods of estimating capacitances.
Finally, for some geometrical configurations of the conducting parts, empirical methods have been developed over the last few decades, which are based on experimental results obtained for simplified geometries and which considerably reduce the amount of computing needed.